Two different lines of inquiry were followed to determine how the cerebral cortex and its efferent regions control eye movements and visuospatial attention. In one, activity of movement neurons of the superior colliculus was studied in relation to saccades evoked by electrical stimulation of either the frontal eye field or the superior colliculus and modified by their temporal proximity to visually evoked saccades. In the other, visual neurons in the posterior parietal cortex were studied using double-step tasks to see how this cortex might maintain spatial accuracy when there was a dissonance between the retinal location of a stimulus and the saccade necessary to acquire that stimulus. Neurons in this region discharged when the monkey made a saccade of the proper direction to acquire a stimulus, whether or not that stimulus lay in the neuron's receptive field as studied in a routine fixation task. Such neurons required the presence of a visual stimulus, suggesting that in the posterior parietal cortex, spatial accuracy is maintained by coordinate transformation of a visual map rather than by the explicit coding of target position in space.